You said your original code is working.
I think you should try using wp_redirect but you can’t output any HTML/Headers for that.
Untested, but try the following:
Note: intentionally missed out the html/body tags…
<?php
require_once('../../../wp-config.php');
require_once('../../../wp-load.php');
global $wpdb;
$feedurl=$_POST['scimp_feed_url'];
$showcategory=$_POST['scimp_show_category'];
$table_name = $wpdb->prefix . 'scimp';
$wpdb->insert( $table_name, array('feedurl' => $feedurl, 'category' => $showcategory));
wp_redirect( home_url( '/form/' ) );
exit();
?>